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%I #3 May 01 2014 02:47:11
%S 1,1,2,5,14,42,132,421,1382,4478,15580,54114,181676,650484,2289320,
%T 8028901,28045302,103229014,372640460,1336511110,4882492452,
%U 17534836812,63692926552,234287550818,868236370364,3281589811404
%N Xcatalans - produced as a self-convolved sequence like Catalan numbers (A000108) but use carryless GF(2)[ X ] polynomial multiplication.
%C Shifts one place left when Xmult-convolved (XMULTCONV) with itself.
%p Xcatalans(30); Xcatalans := proc(upto_n) local a,i,k; a := [1]; for i from 1 to upto_n do a := [ op(a), add(Xmult(a[k],a[i-k+1]), k=1..i)]; od; RETURN(a); end;
%p XMULTCONV := proc(a,b) local c,i,k,n; n := min( nops(a), nops(b) ); c := []; for i from 0 to n-1 do c := [ op(c), add(Xmult(a[k+1],b[i-k+1]), k=0..i)]; od; RETURN(c); end;
%Y For Xmult, see A048720 (Xmult table) or A048631 (Xfactorials). Other self-convolved sequences: A000108, A007460 - A007464, A025192.
%K nonn,easy,eigen
%O 0,3
%A _Antti Karttunen_, May 15 2001
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